The "basic" exponential growth equation is the solution to the
differential equation:
dx/dt = k x(t)
which says the rate of change of x(t) is proportional to x(t), where x(t)
is taken to be the population size at time t.
The solution is:
x(t) = k1 exp(-k2 t)
the constants k1 & k2 depend on K an the initial population size at
time t=0.
For more on population, get the book "[I can't remember the title,
something like"Introduction to Population Genetics"] by Crow & Kimura.
For the binary fission problem, Suppose that at the population size
doubles every generation:
No
N(1) = 2* No
N(2) = 2* N(1) = 2*2*No
N(k) = 2**k * No
Does this help?
Jack